Home
Class 12
MATHS
For two statements p and q, the statemen...

For two statements p and q, the statement `~(pvv(~q))` is equivalent to

A

`~pvvq`

B

`~p^^q`

C

`~pvv~q`

D

`~p^^~q`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem of determining the equivalence of the statement `~(p ∨ (~q))`, we can follow these steps: ### Step 1: Understand the statement We start with the statement `~(p ∨ (~q))`. Here, `~` denotes negation, and `∨` denotes logical OR. ### Step 2: Apply De Morgan's Law According to De Morgan's Law, the negation of a disjunction (OR) can be expressed as the conjunction (AND) of the negations. Therefore, we can rewrite the statement as: \[ ~(p ∨ (~q)) = ~p ∧ ~~q \] ### Step 3: Simplify the double negation The double negation `~~q` simplifies to just `q`. So we can rewrite the expression as: \[ ~p ∧ q \] ### Step 4: Conclusion Thus, the statement `~(p ∨ (~q))` is equivalent to `~p ∧ q`. ### Final Answer The equivalent statement is `~p ∧ q`. ---
Promotional Banner

Similar Questions

Explore conceptually related problems

For any statements p and q , the statement ~(~p^^q) is equivalent to

The statement (~(phArr q))^^p is equivalent to

The statement ~(phArr q) is not equivalent to

The statement p to(q to p) is equivalent to

The statement phArr q is not equivalent to

The statement p vv q is

(~pvv~q) is logically equivalent to

If p and q are two statements, then p vv ~ ( p Rightarrow ~ q) is equivalent to

If p and q are two statements, then p vv ~ ( p Rightarrow ~ q) is equivalent to

If p:''4 is an odd number'' and q : '' 4^(3) is an even number'' are two statements, then which of the following statements is equivalent to ~(prArrq) ?